Naturalism

Naturalism states that we are all completely natural human beings, that there is no immaterial god "out there" and there is no immaterial soul "in here". It also states that freewill is an illusion, that we are as individuals who we are because of our genetics, environment, and culture.

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If it is not possible to determine the position and force of any given particle, as with some popular quantum physics principles, then S(t) is by definition indeterminable and left up to chance, therefore free will is false.

Indeterminability is not the same thing as "left up to chance"—your logic is faulty here.

Indeterminability is by definition left up to chance, for if there were no chance involved, it would be determinable. Why don't you provide an explanation for indeterminability then? Anyone can say something is false without proof.

Glad to explain. I'll choose a classic example—Laplace's Demon. Laplace claimed complete determinism—that the future is completely determined by the past, more or less what you are claiming. He had in mind the movement of astronomical bodies and in particular the solar system.

No one would claim the evolution of the solar system (considered in isolation) is "left to chance" —it follows from the law of gravitation—but neither is it precisely determinable from that law. It is not even known for certain the solar system is stable over the long term. The problem is in part mathematical. Solutions to the n-body problem are approximations and over the long term reality may diverge considerably from calculations.

A system, if we consider the overall system, is said to be determinable if we could predict the outcome with prior knowledge, or indeterminable if we couldn't. That isn't to say we couldn't determine parts of a complex system, some parts of which we could predict, some parts we couldn't -- in fact, this is why it would be useful to break down reducible complex systems into simpler systems for consideration. And all physical matter, whether that which comprise the solar system or the brain could be reduced to subatomic particles.

When it comes to the determinability of a complex system:
Ds is true if D1 AND D2 AND D3 AND... Dn is true

If one component is indeterminable, then the whole system, the solar system, is indeterminable (despite the common understanding that the solar system is determinable, they are not talking about the solar system as a system).

But regardless of what you think about the solar system, I'm sure all serious philosophers would agree the outcome of the solar system is not willed into place. Being indeterminable merely means that we could not deduce an outcome with prior knowledge, making the outcome chance-based. It is by definition and self-evident, aside from an argument of ignorance.

A system, if we consider the overall system, is said to be determinable if we could predict the outcome with prior knowledge, or indeterminable if we couldn't.

That's fine as a definition, but then you go on to contradict it by saying:

Being indeterminable merely means that we could not deduce an outcome with prior knowledge, making the outcome chance-based.

A good counter-example are Steven Wolfram's finite automata, where a simple set of rules produces, after many iterations, quite complex and unpredictable behavior. Outcomes are indeterminable from the rules, but not at all "chance-based."

Again, it is wrong to equate indeterminable with chance-based. Outcomes may be determined (as pure phenomena) without being determinable (involving an observer and predictability).

That's fine as a definition, but then you go on to contradict it by saying:

To contradict means to say x = not x. x = x would be a restatement. If it is acceptable for the definition of determinable to be:

we could predict the outcome with prior knowledge

...then the definition of indeterminable being:

we could not deduce an outcome with prior knowledge

... is the opposite, as determinable and indeterminable are opposites. This is a practical restatement, not a contradiction.

Outcomes may be determined (as pure phenomena) without being determinable (involving an observer and predictability).

These distinctions are superfluous. All physical phenomena are determined, and so we are only interested in whether the outcome is determinable. If an observer with all pertinent prior knowledge of the phenomena could predict an outcome, then it is determinable, otherwise it is indeterminable.

A good counter-example are Steven Wolfram's finite automata, where a simple set of rules produces, after many iterations, quite complex and unpredictable behavior. Outcomes are indeterminable from the rules, but not at all "chance-based."

Wolfram's seemingly random patterns are indeterminable only if you consider the adjacent cells as a series, but they are totally determinable if you know the rules and parameters used to propagate them. An example is the number π(pi) which has seemingly random and unpredictable digits, yet, since we know it is π, the nth digit could be calculated.

Regardless of Wolfram, if there were such thing as a determined but indeterminable outcome (or that any of a set of possible outcomes could arise from the same conditions), that would by definition require chance, for any outcome depends on some fixed logic would be determinable from that logic (tautology because it's self-evident).

We could draw our little plot of outcome possibilities as such:

Determined and determinable - no possible alternative = no free will

Determined and undeterminable - a set of possible alternatives that must require chance, therefore no free will

Undetermined and determinable - impossible, must require God

Undetermined and undeterminable - impossible, must be completely random/chaotic, inconceivable

Quantum indeterminacy describes an indeterminable outcome. You could take a quote out of context and say, because some value described by QI is indetermined at some given time, then it would seem as if I'm dismissing QI by saying all physical phenomena are "determined". This is disingenuous because, in the context of Wolfram, his cellular automata are determined by his rules, but are indeterminable, as your previous argument went. Determined means, then, "caused by a prior state or function", not "has a definite value." The distinction is superfluous because all physical phenomena have exists from a prior state or function, even if it is not determinable at any given moment.

You seem to be very confused. QI does nothing for the argument of free will, as I have detailed over and over -- because you simply can't deny the fact that QI involves chance and a degree of randomness, and the fact that a value is indetermined at some given time is immaterial to the fact that the outcome still requires chance over possible values.

You have been trying to disprove an argument for the lack of free will by arguing over the semantics of "indetermined", which ultimately has nothing to do with the argument whatsoever.

There's a very simple way to attack the logic itself and that is to show how an indeterminable outcome does not involve chance.

Wolfram, or any imaginary numbers, are very much determined by the rules and parameters that define the initial condition. If you use the same rule twice, you will get the same result, even if future results seem unpredictable against prior results.

Oh, I thought naturalist was someone who liked nude vacations. I myself am a naturalist though not because I'm an exhibitionist or voyeur. I'm just lazy and hate doing a bunch of laundry after vacation.